(CNN) -- Hawaii Gov. Linda Lingle vetoed a civil unions bill Tuesday that would have given same-sex couples the same rights as heterosexual couples, saying the issue needs to be put to a referendum.

"I am vetoing this bill because I have become convinced that this issue is of such significant societal importance that it deserves to be decided directly by all the people of Hawaii," Lingle said.

"The subject of this legislation has touched the hearts and minds of our citizens as no other social issue of our day. It would be a mistake to allow a decision of this magnitude to be made by one individual or a small group of elected officials."

Gay rights group decried Lingle's decision.

"Today was the first time a civil unions bill passed both Houses in Hawaii by solid margins and was on the Governor's desk for signing," Jo-Ann Adams, chair of the GLBT Caucus of the Democratic Party of Hawaii, said in a statement. "With such broad support from the legislators, who are the elected officials closest to the public, and the consistent results of the professional polls showing broad support for civil unions as a civil rights issue, we are deeply disappointed that the Governor ignored the will of the people and vetoed the bill. "

Another group, Equality Hawaii, said the fight for equal rights will continue.

"Today is a sad day for the thousands of Hawaii families who remain second class citizens," said Alan Spector, legislative affairs co-chair for Equality Hawaii.

The governor said she understands why supporters of the bill are upset by her decision.

"This is a decision that should not be made by one person sitting in her office or by members of the Majority Party behind closed doors in a legislative caucus, but by all the people of Hawaii behind the curtain of the voting booth," Lingle said in a statement.

"And while some will disagree with my decision to veto this bill, I hope most will agree that the flawed process legislators used does not reflect the dignity this issue deserves, and that a vote by all the people of Hawaii is the best and fairest way to address an issue that elicits such deeply felt emotion by those both for and against."

When the bill passed in April, civil union supporters cheered in the Capitol rotunda. But Lt. Gov. Duke Aiona said at the time lawmakers shouldn't have approved the measure.

"If the legislature wanted to establish the equivalent of same-sex marriage, they should have put it on the ballot for the people to decide," he said then.

Some religious groups had urged the governor to veto the legislation.

"We need you to mount a campaign to flood the governor's office with requests to veto the bill," Larry Silva, Catholic bishop of Honolulu, wrote on the diocese of Honolulu's website at the time.

Five U.S. states and the District of Columbia issue marriage licenses to same-sex couples, according to the National Conference of State Legislatures. Hawaii would join New Jersey in allowing civil unions.

Three states -- Rhode Island, New York, and Maryland -- recognize same-sex marriages from other states, according to the conference.

California recognizes same-sex marriages performed during six months in 2008 after its Supreme Court granted same-sex couples the right to marry and before the passage of Proposition 8, which overturned the court's decision.